Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 1737 and 1742 the smallest integer that is 3025854 that is divisible by both numbers.
Least Common Multiple (LCM) of 1737 and 1742 is 3025854.
LCM(1737,1742) = 3025854
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
Least common multiple can be found by multiplying the highest exponent prime factors of 1737 and 1742. First we will calculate the prime factors of 1737 and 1742.
Prime Factorization of 1737
3 | 1737 |
3 | 579 |
193 | 193 |
1 |
Prime factors of 1737 are 3,193. Prime factorization of 1737 in exponential form is:
1737 = 32×1931
Prime Factorization of 1742
2 | 1742 |
13 | 871 |
67 | 67 |
1 |
Prime factors of 1742 are 2, 13,67. Prime factorization of 1742 in exponential form is:
1742 = 21×131×671
Now multiplying the highest exponent prime factors to calculate the LCM of 1737 and 1742.
LCM(1737,1742) = 21×32×131×671×1931
LCM(1737,1742) = 3025854
Factors of 1737
List of positive integer factors of 1737 that divides 1737 without a remainder.
1, 3, 9, 193, 579, 1737
Factors of 1742
List of positive integer factors of 1742 that divides 1742 without a remainder.
1, 2, 13, 26, 67, 134, 871, 1742
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1737 and 1742, than apply into the LCM equation.
GCF(1737,1742) = 1
LCM(1737,1742) = ( 1737 × 1742) / 1
LCM(1737,1742) = 3025854 / 1
LCM(1737,1742) = 3025854
(i) The LCM of 1742 and 1737 is associative
LCM of 1737 and 1742 = LCM of 1742 and 1737
1. What is the LCM of 1737 and 1742?
Answer: LCM of 1737 and 1742 is 3025854.
2. What are the Factors of 1737?
Answer: Factors of 1737 are 1, 3, 9, 193, 579, 1737. There are 6 integers that are factors of 1737. The greatest factor of 1737 is 1737.
3. What are the Factors of 1742?
Answer: Factors of 1742 are 1, 2, 13, 26, 67, 134, 871, 1742. There are 8 integers that are factors of 1742. The greatest factor of 1742 is 1742.
4. How to Find the LCM of 1737 and 1742?
Answer:
Least Common Multiple of 1737 and 1742 = 3025854
Step 1: Find the prime factorization of 1737
1737 = 3 x 3 x 193
Step 2: Find the prime factorization of 1742
1742 = 2 x 13 x 67
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 3025854 = 2 x 3 x 3 x 13 x 67 x 193
Step 4: Therefore, the least common multiple of 1737 and 1742 is 3025854.